Question

a council has 6 men and 3 women. if we randomly choose two of them to co chair a committee, what is the probability these chairpersons are the same gender

Answer 1

There are a total of 9 women and 6 men on the council, for a total of 15 council members.

If we randomly choose 2 of them to co-chair a committee, the number of ways to choose 2 people of the same gender is:

• The number of ways to choose 2 women out of the 3 women on the council is 3 choose 2 = 3.
• The number of ways to choose 2 men out of the 6 men on the council is 6 choose 2 = 15.

So the total number of ways to choose 2 people of the same gender is 3+15 = 18.

The total number of ways to choose 2 people without considering their gender is 15 choose 2 = 105

So the probability of choosing 2 people of the same gender is 18/105 = 6/35

So, the probability that these chairpersons are the same gender is 6/35.